Programs When Do Math Majors Learn to Master Proofs in Analysis?

[courtrigrad]

When do math majors learn to do proofs? Do they usually learn how to do them in Analysis?

 

[d_leet]

I'm still in high school, but I've been taking math classes at a local college for a while and in their math department they have an introduction to proofs class which is a prerequisite for most of the higher level classes that involve proofs.

 

[ircdan]

When do math majors learn to do proofs? Do they usually learn how to do them in Analysis?

If by analysis you mean advanced calculus then yes that was my first experience with harder proofs. I had seen proofs before in a course in logic and in a course in discrete mathematics, but it was still a big step up. Some people see them first in algebra, or maybe linear algebra, it depends what you take.

The more proof based courses you take, the easier it becomes to write proofs, and the easier it becomes to learn new math you haven't seen before. I think the courses that teach you how to do proofs teach you basic techniques like what to assume and what to show. So they prepare you in a sense, but once you start taking harder courses where all you do is prove results, it's still going to be a lot of work. The trick to do well in a proof based course is to not give up, you're going to get stuck, everyone does. A lot of people work on a problem and if they can't get it done in 20 minutes they give up, that's not how you learn. Sometimes it helps to step away and come back to it later, but you should give it your best effort everytime you approach it(if you have the time to of course). You have to keep trying, it's the "figuring the proof out" part that teaches you how to do proofs.

 

[Muzza]

Er, there are math courses for math majors which don't involve at least some proof writing?

 

[J77]

The trick to do well in a proof based course is to not give up, you're going to get stuck, everyone does. A lot of people work on a problem and if they can't get it done in 20 minutes they give up, that's not how you learn. Sometimes it helps to step away and come back to it later, but you should give it your best effort everytime you approach it(if you have the time to of course). You have to keep trying, it's the "figuring the proof out" part that teaches you how to do proofs.

Yeah - the proof writing stuff just sinks in after a while.

A bit like Complex Analysis - hardly anyone understands the first few lectures - a few can grasp it by the end...

 

[MathematicalPhysicist]

When do math majors learn to do proofs? Do they usually learn how to do them in Analysis?

i would say in the first lecture, after some introductions and definitions you get straight to the proofs.
anyway, you I am quite sure you met proofs already in high school, at least in geometry classes

 

[nocturnal]

Yeah - the proof writing stuff just sinks in after a while.

I think the technical term for this is "by osmosis"

 

[rad0786]

We first learned proofs in "Introduction to Real Analysis" in Second Year.

 

[mathwonk]

as soon as possible. they used to elarn them in high school geometry from euclidean geometry. unfortunately this went out when teqchers decided stupoidly that proofs were too hard for sonme of their stduents and in order to keep the cousre democratic, they tried to make it easier so there would be no differenbce in the performance of smart and stupid students. makes sense huh? they lowoer the basket for weak basketball players righta? no? geee, whaTS UP THERE?anyway, get a book with prof in it and start readint them and elarning how to do them. i used principles of mathematics by allendoerfer and oakley, and klater what is amhematics by courant and robbins, and diif and integral calculus by courant, and many other books.read my algebra book or my baby algebra book, all free online on my website, but start now. you cab do it, you are smart, it is the etachers that watered down the subject, not the students.

 

[CPL.Luke]

I learned some proof working in geometry class, but the importance and depth was completely absent from the unit, everyone I knew at the time just found them to be an annoying little subject with no purpose.

 

[MathematicalPhysicist]

you learn geometry in school without proving theorems?!

 

[BryanP]

The first time I started doing proofs regularly in any class was when I took upper division linear algebra (Math 110 @ UC Berkeley). Pretty much almost all the homework problems I did had to do with proving stuff and it hasn't changed too much ever since. My introduction to Analysis class (Math 104) has plenty of it, as well as my Elementary Abstract Algebra class (Math 113).

However, when it came to doing proofs here or there, that started way back (my 10th grade teacher was a nut! but I thank him for the early-start). My discrete math class (math 55) in college had a good chunk of proof-writing as well.

 

[Bitter]

I was introduced proofs during high school in Geometry. I didn't think much of them at the time. When I took Calc 1 in college, that is when they started to be forced on me. My Professor would make use prove certain facts with theorems we learned and should know. It was difficult for me because I couldn't remember any of the theorems, but after a while, it became easier.

 

[kramer733]

as soon as possible. they used to elarn them in high school geometry from euclidean geometry. unfortunately this went out when teqchers decided stupoidly that proofs were too hard for sonme of their stduents and in order to keep the cousre democratic, they tried to make it easier so there would be no differenbce in the performance of smart and stupid students. makes sense huh? they lowoer the basket for weak basketball players righta? no? geee, whaTS UP THERE?

That's a major fallacy. I live in Canada and EVERY math or physics teacher i talked to have wanted to bring back proofs in mathematics. It's the school board that decides all this and they decided to take proofs out.

 

[snipez90]

Well that's because you live in Canada. Mathwonk is an American mathematician, so in all likelihood he was discussing in the context of the American mathematics education system. Of course he was making a generalization, but you probably also know how the American education system fares compared to others, so I wouldn't say he committed any fallacies.

But then again Mathwonk has long since left the forums, and this is a almost 4 year old thread, so what the hell.

 

[Ben1220]

lol at m-m-m-m-mmmmonster bump

and if anyone still cares, there were some proofs in calc 1&2 and linear algebra, but we weren't expected to derive them ourselves usually or do our own proofs. That started in real analysis.

 

[kramer733]

Ooops sortry guys. I was browsing threads at the bottom of the pages under "quick reply"